An enhanced component connection method for conversion of fault trees to binary decision diagrams

Abstract

A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk An Enhanced Component Connection Method for Conversion of Fault Trees toBinary Decision Diagrams R. Remenyte-Prescott; Prof. J.D. Andrews AbstractFault Tree Analysis (FTA) is widely applied to assess the failure probability of industrial systems. Many computer packages are available which are based on conventional Kinetic Tree Theory methods. When dealing with large (possibly non-coherent) fault trees, the limitations of the technique in terms of accuracy of the solutions and the efficiency of the processing time becomes apparent. Over recent years the Binary Decision Diagram (BDD) method has been developed that solves fault trees and overcomes the disadvantages of the conventional FTA approach. First of all, a fault tree for a particular system failure mode is constructed and then converted to a BDD for analysis. This paper analyses alternative methods for the fault tree to BDD conversion process.For most fault tree to BDD conversion approaches the basic events of the fault tree are placed in an ordering. This can dramatically affect the size of the final BDD and the success of qualitative and quantitative analyses of the system. A set of rules are then applied to each gate in the fault tree to generate the BDD. An alternative approach can also be used, where BDD constructs for each of the gate types are first built and then merged to represent a parent gate. A powerful and efficient property, sub-node sharing, is also incorporated in the enhanced method proposed in this paper. Finally a combined approach is developed taking the best features of the alternative methods. The efficiency of the techniques is analysed and discussed.Keywords: Fault Tree Analysis, Binary Decision Diagrams IntroductionThe Binary Decision Diagram (BDD) method [1] has been introduced as a method for efficient and accurate fault tree analysis. This method has been shown to have advantages over the conventional Kinetic Tree Theory [2]. The main strength of the BDD method is the fact that top event probabilities can be calculated without the need to apply approximations or the need to obtain minimal cut sets as intermediate results.In the BDD method the fault tree is converted to a binary decision diagram, which represents the Boolean logic expression of the particular system failure mode. The method requires to set the variable ordering, and if it is not chosen suitably, the size of the final BDD can grow exponentially. The ordering rules are then applied to construct the BDD (ite method [1]). Alternative conversion methods are presented in this paper. These include component connection methods [3] where BDDs for each of the gate types are formed and then ...

Fault tree analysis: A survey of the state-of-the-art in modeling, analysis and tools

“…We require [39] BDD Only for coherent FTs but faster than [37] Aralia [40] Dutuit and Rauzy [41] Modular BDD Faster for FTs with independent submodules DIFTree [42] Remenyte et al [43,44] BDD Comparison of BDD construction methods -Codetta-Raiteri [45] BDD Faster when FT has shared subtrees -Xiang et al [46] Minimal Cut Vote Reduced complexity with large voting gates CASSI [46] Carrasco et al [47] CS-Monte Carlo Less complex for FTs with few MCS -Vesely and Narum [48] Monte Carlo Low memory use, accuracy not guaranteed PREP [48] Some analysis methods described in Sections 2.2 and 2.3 require the undirected graph ⟨E, I⟩ to be a tree, i.e., forbid shared subtrees. In this paper, an FT will be considered a DAG.…”

“…Remenyte and Andrews [43,44] have compared several different methods for constructing BDDs from FTs, and conclude that a hybrid of the if-then-else method [39] and the advanced component-connection method by Way and Hsia [54] is a good trade-off between processing time and size of the resulting BDD. Improvements to BDD.…”

System reliability assessment incorporating interface and function failure

“…Andrews (2002) [8] proposed an analysis strategy aimed at increasing the likelihood of obtaining the BDD for any given fault tree with both complex and modular events. Remenyte and Andrews (2008) [9] analyzed alternative methods for the fault tree to BDD conversion process and proposed an enhanced component connection method. Dutuit and Rauzy (2005) [10] consider four algorithms for estimating the system reliability via fault trees and compared their performances with a Markovian analysis on various examples and showed that approximations are accurate and the algorithms are efficient in terms of computation times.…”

“…(5) ; (6) ; (7) ; (8) ; (9) ; (10) At the first, the top-down substitution will be performed, starting with the top event equation and substituting and expanding until the minimal cut set expression for the top event is obtained. Substituting for and and expanding we have:…”

The mechanical generation of fault trees for reactive systems via retrenchment II: clocked and feedback circuits

“…Regarding the algorithms for fault tree generation used in FSAP, the minimisation routines used to extract the set of minimal cut sets are based on classical procedures for minimisation of Boolean functions, specifically on the implicit-search procedure described in [CM92,CM93,Rau93,RD97], based on BDDs [Bry92] (see also [RPA08] for enhanced methods to convert fault trees into BDDs). Alternative explicit-search and satisfiability based techniques for computation of prime implicants are described, e.g.…”